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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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You are working during the summer at a company that builds theme parks. The company is designing an electromagnetic propulsion system for a new roller coaster. A model of a substructure of the device appears in the figure below.

Two parallel, horizontal rails extend from left to right, with one rail behind the other. A cylindrical rod rests on top of and perpendicular to the rails at their left ends. The distance between the rails is d and the length of the rails is L. The magnetic field vector B points vertically down, perpendicular to the rails. Within the rod, the current I flows out of the page, from the rail in the back toward the rail in the front.

The rod is of length d = 1.00 m and mass m = 0.600 kg. The rod carries a current I = 100 A in the direction shown and rolls along the rails of length L = 20.0 m without slipping. The entire system of rod and rails is immersed in a uniform downward-directed magnetic field with magnitude B = 2.00 T. The electromagnetic force on the rod is parallel to the rails, causing the rod to roll to the right in the figure. When a full-scale device is produced, this rod will represent the axle of wheels on which the car and its passengers ride. The electromagnetic force on the axle will provide the motion of the car at the beginning of the roller-coaster ride. Your supervisor wants to test the substructure in the figure in a flat outdoor area on the grounds of the company. By projecting the rod from the rails in a horizontal direction from a height h = 2.00 m, the projection speed can be determined from how far from the ends of the rails the rod hits the ground. Your supervisor asks you to determine the length of the outdoor area needed to test the device. (Determine the total horizontal distance, in m, from the initial position of the rod on the tracks to the final position of the rod where it lands on the ground.)

### Description of the Diagram:

The diagram illustrates the interaction between a current-carrying conductor and a magnetic field, depicting the principles behind electromagnetism. It showcases how the movement of a conductor within a magnetic field induces an electromagnetic force.

### Key Components:

1. **Current-Carrying Rod (Conductor):**
- Represented as a cylindrical rod placed at a certain angle within the magnetic field.
- The current \( I \) is depicted by an arrow along the rod, indicating the direction of flow.

2. **Magnetic Field (\( \mathbf{B} \)):**
- Illustrated by vertical green arrows pointing downwards.
- The direction of the arrows signifies the direction of the magnetic field lines, which are perpendicular to the plane of the conductor.

3. **Rails/Tracks:**
- The rod rests on two parallel rail tracks.
- The distance between the two tracks is denoted by \( d \).

4. **Length of the Rod:**
- The length of the rod is labeled \( L \).

### Explanation:

- The setup is used to demonstrate the concept of electromagnetic induction or the Lorentz force.
- As the rod carries an electric current in the presence of a magnetic field, a force is exerted on it due to the \( \mathbf{I} \times \mathbf{B} \) interaction.
- This force can cause the rod to move along the rails, illustrating the basic principle of electric motors.

This configuration is fundamental in understanding how electric engines, generators, and related technologies function, emphasizing the conversion of electrical energy to mechanical movement.

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